Sunday Times Teaser 2923 – Powerful Numbers

by Danny Roth

Published September 30 2018 (link)

George and Martha’s five daughters have been investigating large powers of numbers. Each daughter told the parents that they had worked out a number which was equal to its last digit raised to an exact power. When Andrea announced her power, the parents had a 50% chance of guessing the last digit. When Bertha announced a larger power, the same applied. When Caroline announced her power, the parents had only a 25% chance of guessing the last digit; with Dorothy’s larger power, the same applied. When Elizabeth announced hers, the parents only had a 12.5% chance of guessing the last digit. I can tell you that the five powers were consecutive two-digit numbers adding up to a perfect square.